In this study, we consider the geometric aspects of low earth orbit (LEO) satellite constellations and investigate the performance of a satellite network that uses our proposed routing algorithm. The optimum inclination and harmonic factor of rosette constellations are obtained by considering the minimum coverage radius of a satellite. Actual altitude is determined by this radius and the specified elevation angle. The algorithm uses the uniformity of the geometric structure to form a continuously connected group of nodes in the network which renders global intersatellite connectivity information insignificant. Each group, consisting of a node and its four neighbours, does not change with time and a stationary network structure is obtained by allowing each node to communicate only with its neighbours. Queuing analysis of the network is made for both packet and voice traffic. Simulation results are then compared to analytical results derived from uniform ciricl equal traffic distribution. The proposed algorithm is simulated in a scenario in which sources, destinations, and gateways on the earth form the global traffic. We examine the effects of such a distribution on the performance of the network.